On a Three-Step Efficient Fourth-Order Method for Computing the Numerical Solution of System of Nonlinear Equations and Its Applications

摘要

In this paper, a new fourth-order iterative scheme for finding the zeros of systems of nonlinear equations has been built and analyzed. Theoretical proof has been given to confirm the convergence order of the new method. The effectiveness of the proposed method is shown by the comparison of traditional as well as flops-like efficiency index with recent existing same order schemes. Numerical examples confirm that the new iterative method is efficient and gives tough competition to some existing fourth-order methods. We have also discussed the application of our proposed method for finding numerical solution of nonlinear ODE and PDE.